# Sufficient Stability Conditions for Time-varying Networks of Telegrapher's Equations or Difference Delay Equations

3 McTAO - Mathematics for Control, Transport and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We give a sufficient condition for exponential stability of a network of lossless telegrapher's equations, coupled by linear time-varying boundary conditions. The sufficient conditions is in terms of dissipativity of the couplings, which is natural for instance in the context of microwave circuits. Exponential stability is with respect to any $L^p$-norm, $1\leq p\leq\infty$. This also yields a sufficient condition for exponential stability to a special class of linear time-varying difference delay systems which is quite explicit and tractable. One ingredient of the proof is that $L^p$ exponential stability for such difference delay systems is independent of $p$, thereby reproving in a simpler way some results from [3].
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Journal articles
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https://hal.inria.fr/hal-02385548
Contributor : Jean-Baptiste Pomet <>
Submitted on : Tuesday, January 19, 2021 - 12:05:53 PM
Last modification on : Wednesday, January 20, 2021 - 3:36:05 AM

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papier_SIMA_stab_HAL.pdf
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### Identifiers

• HAL Id : hal-02385548, version 3
• ARXIV : 1911.13003

### Citation

Laurent Baratchart, Sébastien Fueyo, Gilles Lebeau, Jean-Baptiste Pomet. Sufficient Stability Conditions for Time-varying Networks of Telegrapher's Equations or Difference Delay Equations. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, inPress. ⟨hal-02385548v3⟩

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